On 2/19/08, Ryan Ingram
Oleg's done a lot of work here; there's a bunch of magic that can be done with TypeCast. I took my inspiration from here: http://okmij.org/ftp/Haskell/typecast.html#ambiguity-resolution
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The trick is to represent whether a type is boxed or not via a
type-level boolean, which you can then use to affect the instance selecton.
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-- Magic toolbox that solves everything! Thanks Oleg!
data HTrue data HFalse
class TypeCast a b | a -> b, b->a where typeCast :: a -> b class TypeCast' t a b | t a -> b, t b -> a where typeCast' :: t->a->b class TypeCast'' t a b | t a -> b, t b -> a where typeCast'' :: t->a->b instance TypeCast' () a b => TypeCast a b where typeCast x = typeCast' () x instance TypeCast'' t a b => TypeCast' t a b where typeCast' = typeCast'' instance TypeCast'' () a a where typeCast'' _ x = x
Thanks for showing me this technique. I studied your code for several hours. And, I've read Oleg's "Strongly Typed Heterogeneous Collections." As a learning exercise, I modified your code. I managed to shorten it a bit, but I had a couple of surprises. Please see my comments in the code below. {-# OPTIONS_GHC -fglasgow-exts -fbreak-on-exception -fallow-undecidable-instances -fallow-overlapping-instances #-} module SmartArray where import IO import Data.Ix import Data.Array.Unboxed import Data.Complex type SmartArray i e = (Ix i, SmartArraySelector a e) => (a i e) -- smartArray is similar to array function from Data.Array. But, -- it will return a UArray if e can be unboxed. Otherwise, it -- returns an Array. smartArray :: (i, i) -> [(i, e)] -> SmartArray i e smartArray bnd eLst = array bnd eLst class ArrTypeCast a b | a -> b, b->a where arrTypeCast :: a i e -> b i e instance ArrTypeCast x x where arrTypeCast = id -- SURPRISE 1: If function, arrTypeCast, is removed, (from both -- the class and instance) GHC assumes the kind of a and b are *, -- instead of * -> * -> * and produce . . . -- -- report3.hs:37:24: -- `UArray' is not applied to enough type arguments -- Expected kind `*', but `UArray' has kind `* -> * -> *' -- In the type `(ArrTypeCast a UArray, IArray a Bool) => -- SmartArraySelector a Bool' -- In the instance declaration for `SmartArraySelector a Bool' -- -- It appears that functions defined in a class can constrain the -- type variables of the class. To me, this seems a bit magical -- and unexpected. class (IArray a e) => SmartArraySelector a e | e -> a -- instances of SmartArraySelector for all boxed types (For -- breivity, not all unboxed types are listed.) instance (ArrTypeCast a UArray, IArray a Bool) => SmartArraySelector a Bool instance (ArrTypeCast a UArray, IArray a Char) => SmartArraySelector a Char instance (ArrTypeCast a UArray, IArray a Double) => SmartArraySelector a Double instance (ArrTypeCast a UArray, IArray a Float) => SmartArraySelector a Float instance (ArrTypeCast a UArray, IArray a Int) => SmartArraySelector a Int -- SURPRISE 2: The class SmartArraySelector has the type -- assertion, (IArray a e). It seems like adding an additional -- IArray assertion to each instance is redundant. However, -- if I remove the assertion (IArray a Int) above, GHC -- reports . . . -- -- report3.hs:37:24: -- `UArray' is not applied to enough type arguments -- Expected kind `*', but `UArray' has kind `* -> * -> *' -- In the type `(ArrTypeCast a UArray, IArray a Bool) => -- SmartArraySelector a Bool' -- In the instance declaration for `SmartArraySelector a Bool' -- -- Why is this second type assertion required? instance (ArrTypeCast a Array, IArray a b) => SmartArraySelector a b test :: SmartArraySelector a e => e -> a Int e test e = smartArray (0,10) [ (i,e) | i <- [0..10]] I'd love to find a good article that describes the ins and outs of multi parameter types, functional dependencies, and type assertions, in enough detail to resolve these surprises. A step-by-step walk through showing how the compiler resolve a type and selects an instance would be awesome. Usually, when I'm having trouble getting Haskell's type system to do what I want, I resort to trial and error tactics. I wish I had a better foundation so I could take a more intelligent approach to type hacking.